Results 51 to 60 of about 717 (185)

Liouville-Green approximations via the Riccati transformation

Journal of Mathematical Analysis and Applications, 1986
Consider the scalar second order equation on (a,b) \(u''=f(t)u\) with \(f(t)=p(t)^ 2+q(t)\) or \(f(t)=-p(t)^ 2+q(t),\) being p positive and piecewise differentiable and q piecewise continuous. Under suitable conditions on f, using a Riccati transformation, fundamental solutions are found and these are used to provide Liouville-Green approximations and ...
openaire   +2 more sources

Advanced control of non‐isothermal axial dispersion tubular reactors with recycle‐induced state delay

The Canadian Journal of Chemical Engineering, Volume 104, Issue 6, Page 3018-3037, June 2026.
Abstract We develop a delay‐aware estimation and control framework for a non‐isothermal axial dispersion tubular reactor modelled as a coupled parabolic‐hyperbolic PDE system with recycle‐induced state delay. The infinite‐dimensional dynamics are preserved without spatial discretization by representing the delay as a transport PDE and adopting a late ...
Behrad Moadeli, Stevan Dubljevic
wiley   +1 more source

Kamenev-type oscillation criteria for forced Emden-Fowler superlinear difference equations

Electronic Journal of Differential Equations, 2002
Using Riccati transformation techniques, we establish oscillation criteria for forced second-order Emden-Fowler superlinear difference equations. Our criteria are discrete analogues of the criteria used for differential equations by Kamanev [5].
Samir H. Saker
doaj  

Exact Solutions and Nonlinear Dynamical Behavior in a Navier‐Stokes‐Type Model for Elastic Cylindrical Vessels: An Analytical and Computational Approach

Engineering Reports, Volume 8, Issue 6, June 2026.
This study investigates a nonlinear Navier‐Stokes‐type model for elastic cylindrical vessels. Exact solutions are derived via the Bäcklund transformation and the ϕ6$$ {\phi}^6 $$‐expansion method, and dynamical behaviors are analyzed using bifurcation and chaos tools, revealing diverse wave structures and parameter‐dependent propagation characteristics.
Sheikh Zain Majid, Fatma Nur Kaya Sağlam, Mohammad Safi Ullah   +2 more
wiley   +1 more source

Oscillation of second order neutral dynamic equations with distributed delay

Electronic Journal of Qualitative Theory of Differential Equations, 2016
In this paper, we establish new oscillation criteria for second order neutral dynamic equations with distributed delay by employing the generalized Riccati transformation.
Qiaoshun Yang, Zhiting Xu, Ping Long
doaj   +1 more source

Analytical and Numerical Soliton Solutions of the Shynaray II‐A Equation Using the G′G,1G$$ \left(\frac{G^{\prime }}{G},\frac{1}{G}\right) $$‐Expansion Method and Regularization‐Based Neural Networks

Mathematical Methods in the Applied Sciences, Volume 49, Issue 9, Page 9814-9831, June 2026.
ABSTRACT Nonlinear differential equations play a fundamental role in modeling complex physical phenomena across solid‐state physics, hydrodynamics, plasma physics, nonlinear optics, and biological systems. This study focuses on the Shynaray II‐A equation, a relatively less‐explored parametric nonlinear partial differential equation that describes ...
Aamir Farooq, H. W. A. Riaz, Sadique Rehman, M. Mamun Miah, Wen Xiu Ma   +4 more
wiley   +1 more source

Bäcklund Transformation of Fractional Riccati Equation and Infinite Sequence Solutions of Nonlinear Fractional PDEs

Abstract and Applied Analysis, 2014
The Bäcklund transformation of fractional Riccati equation with nonlinear superposition principle of solutions is employed to establish the infinite sequence solutions of nonlinear fractional partial differential equations in the sense of modified ...
Bin Lu
doaj   +1 more source

On the Computation of Tensor Functions under Tensor‐Tensor Multiplications with Linear Maps

Numerical Linear Algebra with Applications, Volume 33, Issue 3, June 2026.
ABSTRACT In this paper, we study the computation of both algebraic and non‐algebraic tensor functions under the tensor‐tensor multiplication with linear maps. In the case of algebraic tensor functions, we prove that the asymptotic exponent of both the tensor‐tensor multiplication and the tensor polynomial evaluation problem under this multiplication is
Jeong‐Hoon Ju, Susana López‐Moreno
wiley   +1 more source

Novel approaches to the construction of solitons in Fokas fiber-optic models

AIP Advances
The Fokas system plays a pivotal role in modeling nonlinear pulse propagation through monomode optical fibers, with exact solutions offering critical insights into the physical mechanisms governing excitation instability.
Guojiang Wu, Chunyan Wang
doaj   +1 more source

Oscillation Criteria of Third-Order Nonlinear Damped Dynamic Equations on Time Scales

Discrete Dynamics in Nature and Society, 2015
We establish oscillation criteria of third-order nonlinear damped dynamic equations on time scales of the form r1tr2txΔtγΔΔ+ft, xt,xσt, xgt, xΔt=0 by employing functions in some function classes and the generalized Riccati transformation.
Yang-Cong Qiu
doaj   +1 more source